Thanks for looking into this, and for the links - I will check these out to see where I am going wrong.
I will send you login details for each of the PS4 and PCMS via my support ticket, and you can see the problem I'm having.
For the Power Gallery image paths problem, - the files are FTPd directly to the remote server, they don't go anywhere near DreamWeaver or its site definition.
For the HTML Editor paths, the local and remote site settings for a site with a simple HTML Instance uploaded seem to me to be correct (see the attached images). I checked the WebAssist/Forms/HTMLEditor/Site Settings, and the value entered was: htmleditor3/files. The file was selected by browsing to the folder in Dreamweaver. If I do the same again, it produces : /htmleditor3/files (which would be correct relative to site root). I reuploaded all files and tried again, but still no go. I went back to Dreamweaver and checked Site Settings (as above) again. The folder path was reset back to: htmleditor3/files.
Every time I do the 'browse to folder', it puts /htmleditor3/files in the field provided, but whenever I save it, it drops the slash. If I remove the 'htmleditor3/' bit - so that the path is at least relative to the document i.e: 'files' - that doesn't save either.
The HTMLEditor styles problem is apparently not a problem, but an enhancement. Ray has pointed out that I may have misunderstood enhancement.
What is particularly irksome is the certain knowledge that it will turn out in each case to be something particularly dumb that I have done.